Many aspects of protein motion can be comprehended with coarse-grained models. Our hypothesis is that atomic detail is not required to explain many aspects of protein behavior, and this simplification can facilitate a deeper understanding. The overall goal is to develop an understanding of how protein motions and function are contolled by structure, why protein sequences fold to a limited set of structures, and to establish the roles of tight packing and the shapes of proteins on their motions. In this project we will investigate the relationships among motions, shapes, structures, interactions and levels of cooperativity. Aim I: Modeling protein dynamics with Elastic Networks. We will use elastic network models to study how proteins restrict their motions to the motions most essential for function. Normal mode analyses will be performed to discern these important functional motions with high computational efficiency to develop molecular mechanisms. We will investigate the atomic motions in active sites of enzymes to see how the large domain motions control the atom movements. We will use elastic networks to interpret single molecule pulling experiments and predict the order in which proteins unravel. Preliminary results show that elastic network models are applicable not only to fluctuations around native conformations, but also to transient states arising when an external force is applied to deform a protein and break its native contacts. These results suggest that structure controls the global motions of proteins, even for transient states. To further verify this hypothesis we will perform more single molecule pulling simulations, and structural analyses of transient protein conformations along folding pathways. The major successes achieved with the elastic models rely upon having good representations of the packing density and protein shape, which we will investigate in Aim II. Aim II: Modeling Protein Packing and Cooperativity of Interactions. Dense packing of residues in proteins is one of their most important characteristic features. We plan to continue our studies of internal packing. The emphasis for new potentials will be on the relative orientations of amino acids in proteins. We will develop many-body contact potentials for identifying native structures among decoys in threading, and also study orientational distributions within clusters of nearby residues in proteins, using regular polyhedra such as icosahedra, or Catalan solids such as tetrakis hexahedra. Our rationale is to use various polyhedral models to comprehend protein packing and amino acid interactions for developing improved many-body potentials. A better understanding of the cooperativity of interactions within proteins is extremely important because this directly influences the ways in which proteins move and respond to forces. Both Aims are highly interconnected and will significantly advance our knowledge of protein structure, dynamics and function.